Paired t test also called as dependent / correlated t-test. It is performed on the same set of samples and their datas measured on different occations. For example, there may be instances of the same patients being tested repeatedly—before and after receiving a particular treatment. Physiotherapist wants to check his mobilization technique on set of peoples for a particular number of sessions. So, he can measure before and after effects of treatment through the paired t test by using pre treatment and post treatment datas.
\[t = \frac{\bar{D}\sqrt{n}}{S}\]
Where\[S = \sqrt{\frac{\sum \left(D - \bar{D}\right)^2}{n-1}}\]